Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics, and electrical spin-manipulation. However, the influence of the graphene environment on the spin systems has yet to be unraveled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. While the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly-developed model. Coupling to Dirac electrons introduces a dominant quantum-relaxation channel that, by driving the spins over Villain’s threshold, gives rise to fully-coherent, resonant spin tunneling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin-manipulation in graphene nanodevices.